Li, Xiaoxia; Han, Danfu A family of iteration with third order convergence. (Chinese. English summary) Zbl 1087.65563 J. Zhejiang Univ., Sci. Ed. 31, No. 3, 253-257 (2004). Summary: A family of iterations for solving nonlinear operator equations in Banach space is presented. The family of iteration avoids evaluating the second Fréchet derivative, but it has convergence of three-orders. The convergence theorem is established using the majorant method, and meanwhile, the sharp estimates are also given. MSC: 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators Keywords:majorizing function; \(\gamma\)-condition; iteration; nonlinear operator equation; Banach space PDFBibTeX XMLCite \textit{X. Li} and \textit{D. Han}, J. Zhejiang Univ., Sci. Ed. 31, No. 3, 253--257 (2004; Zbl 1087.65563)